Answer to Question #99296 in Electrical Engineering for Hardi Amiru Sulemana

Question #99296
An engine operating on the outo cycle has a compression ratio of 7.5:1. At the beginning of the compression stroke,the air is at 1.035bar and 27°C. If the heat energy supplied is 930Kj/kg of air, calculate; the maximum temperature and pressure in the cycle and the cycle efficiency
1
Expert's answer
2019-11-25T07:26:55-0500

The Otto cycle consists of four stages:

1-2: adiabatic compression;

2-3: isochoric compression;

3-4: adiabatic expansion;

4-1: isochoric cooling.



Calculate the cycle thermal efficiency (for the air at the temperature of 27°C k=1.4):


"\\eta_{th}=1-\\frac{1}{r^{k-1}}=1-\\frac{1}{7.5^{1.4-1}}=0.553."

At the end of the adiabatic compression:


"T_2=T_1r^{k-1}=(273+27)7^{1.4-1}=671\\text{ K}."


The pressure at 2 is


"p_2=r\\frac{T_2}{T_1}p_1=7.5\\cdot\\frac{671}{300}\\cdot101325=1736213\\text{ Pa}."

The isochoric heat capacity:


"c_V=2.5\\cdot0.2871=0.71775\\text{ kJ\/(kg-K)}."

The heat energy supplied:


"930=q=c_V(T_3-T_2),"

here "T_3" is the maximum temp:


"T_3=\\frac{q}{C_V}+T_2=\\frac{930}{0.71775}+653=1949\\text{ K}."

During the isochoric stage 2-3 the pressure reaches its maximum as well:


"\\frac{p_2}{T_2}=\\frac{p_3}{T_3},\\\\\n\\space\\\\\np_3=p_2\\frac{T_3}{T_2}=1736213\\frac{1949}{653}=5043038\\text{ Pa},"

or 50.4 bar.


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